## Bohr Model of the Hydrogen Atom – Class 12 | Chapter – 12 | Physics Short Notes Series PDF for NEET & JEE

Bohr Model of the Hydrogen Atom: The Bohr model of the hydrogen atom, proposed by Danish physicist Niels Bohr in 1913, was the first successful attempt to explain the electronic structure of atoms. The model was based on classical physics, but incorporated some key concepts from quantum mechanics, which was still in its infancy at the time.

In the Bohr model of the hydrogen atom, the electron in a hydrogen atom moves in a circular orbit around the nucleus, which consists of a single proton. The size and energy of the electron’s orbit are quantized, meaning they can only take on certain discrete values. The energy of the orbit is related to its distance from the nucleus, with larger orbits having higher energy.

Bohr postulated that the electron in the hydrogen atom could only occupy certain allowed energy levels, and that when the electron changed from one energy level to another, it would emit or absorb a photon of a specific energy. The energy of the photon would be equal to the difference in energy between the two energy levels.

The Bohr model was able to explain many of the properties of the hydrogen atom, including its line spectrum, which was observed experimentally. However, it had several limitations, including the fact that it only applied to the hydrogen atom and could not be generalized to more complex atoms. Additionally, it did not fully explain the wave-like behavior of electrons, which was a key concept in the development of modern quantum mechanics. Nevertheless, the Bohr model was an important milestone in the development of atomic theory, and it laid the groundwork for the development of more sophisticated models of the atom.

## Formula of Bohr Model of the Hydrogen Atom

The energy levels of the hydrogen atom were given by the formula:

E = -13.6 eV/n2

Where,

• E is the energy of the level,
• n is a positive integer known as the principal quantum number, and
• eV is an electron volt, a unit of energy commonly used in atomic physics

## Postulates of Bohr Model of the Hydrogen Atom

The Bohr model of the hydrogen atom is based on a number of postulates, which are as follows:

• Electrons in the hydrogen atom move in circular orbits around the nucleus. The orbits are quantized, meaning that they can only have certain discrete values of energy and angular momentum.
• The energy of an electron in a particular orbit is given by the formula: E = -13.6 eV/n2
• E is the energy of the level,
• n is a positive integer known as the principal quantum number, and
• eV is an electron volt, a unit of energy commonly used in atomic physics
• Electrons can only move from one energy level to another by absorbing or emitting a photon of energy equal to the difference in energy between the two levels.
• When an electron moves from a higher energy level to a lower energy level, it emits a photon with a frequency that is proportional to the energy difference between the levels. Conversely, when an electron absorbs a photon, it moves to a higher energy level.
• The angular momentum of an electron in an orbit is quantized, and is given by the formula: L = nħ
• where L is the angular momentum,
• n is the principal quantum number, and
• ħ is the reduced Planck constant.

## Limitations of Bohr Model of the Hydrogen Atom

The Bohr model of the hydrogen atom was a significant advance in the understanding of atomic structure, but it had several limitations, including:

• The model only applies to the hydrogen atom: The Bohr model is specific to the hydrogen atom, and does not apply to more complex atoms, which have more than one electron. The model does not explain the spectral lines of other atoms or the structure of molecules.
• The model assumes circular orbits: The Bohr model assumes that electrons move in circular orbits around the nucleus, which is not consistent with the wave-like behavior of electrons observed in experiments.
• The model does not account for the electron spin: The Bohr model does not account for the intrinsic angular momentum of electrons known as spin, which is an important property of electrons in atoms.
• The model violates the Heisenberg uncertainty principle: The Bohr model assumes that electrons have a well-defined position and momentum at all times, which violates the Heisenberg uncertainty principle.
• The model does not explain chemical bonding: The Bohr model does not explain how atoms bond to form molecules, which is a crucial aspect of chemistry.

Despite its limitations, the Bohr model of the hydrogen atom was an important step in the development of atomic theory and provided a foundation for more sophisticated models of the atom, such as the quantum mechanical model.

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